Prove that \(\displaystyle{\int_{{{2017}}}^{{{2018}}}}{\left({\arctan{{\left({\ln{{\left({x}\right)}}}\right)}}}-{\ln{{\left({\arctan{{\left({x}\right)}}}\right)}}}\right)}{\left.{d}{x}\right.}{>}{0}\)

abitinomaq1

abitinomaq1

Answered question

2022-03-30

Prove that 20172018(arctan(ln(x))ln(arctan(x)))dx>0

Answer & Explanation

davane6a7a

davane6a7a

Beginner2022-03-31Added 8 answers

For x>e2,
arctan(lnx)>arctan(lne2)=arctan2
>arctan3=π3>1>lnπ2>ln(arctanx)

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